119. If 5 bushels of the corn meal were used, how much would be required of each of the others? Prove.

120. A grocer has four sorts of sugar, worth 4 cts., 5 cts., 7 cts., and 8 cts. a pound. He would make a mixture of 200 lbs., worth 6 cts. a pound? What quantity must be taken of each sort? Prove.

121. A goldsmith has four sorts of gold, namely, of 22 carats fine, of 20 carats fine, of 18 carats fine, and of 15 carats fine. He would make a mixture of 48 oz. of 17 carats fine. How many oz. of each sort must he take? Prove.

122. Afterwards, of the same material, he wished to make a mixture of the same fineness, containing 4 oz. of 20 carats fine. How many ounces must he take of each of the other sorts? Prove.

123. A rectangular field was 16 rods long and 12 wide. How many square rods did it contain ?

124. What is the width of a rectangular field containing 192 square rods, whose length is 16 rods?

125. There are 192 rods in a rectangular field, whose width is 12 rods. What is its length?

126. There is a square field whose sides are 16 rods long. How many square rods does it contain?

127. What is the length of a square field containing 256 square rods?

128. The sides of one of the square fields of a farm is 40 rods long, and those of another 80. How many times is the one larger than the other?

129. There are two square fields in a farm, one of which is 40 rods long; the other is 4 times the size. What is the length of its sides?

130. The inside of a box is 2 feet every way. How many cubical feet does it contain ?

131. The contents of a box with equal sides are 8 cubical feet. What are its length, width, and depth inside?

132. A farmer erected a stable 50 feet long by 25 feet wide. The height of the gable was 8 feet. The eaves projected a foot over each side of the building, and the roof was 2 feet longer than the frame, so as to project a foot over each gable. How many thousand shingles would be required for the roof, if one thousand shingles cover 10 feet square? Ans. 18 nearly.

133. One man exchanged with a broker £4 10s. 10d. sterling for 11 crowns and 7 dollars; and another man, at the same rate, £1 15s. for 4 crowns and 3 dollars. How much were the crown and dollar severally valued at? Prove by trial.

Suggestive Questions.-What is 3 times the amount of the first exchange? 7 times the amount of the 2d? What is the difference between the exchanges thus increased? What, then, is the value of a crown? Of a dollar? In what respects does this operation differ from bringing fractions to the same denomination ?

134. Required two such numbers that if of the first be added to of the second, the sum shall be 66; and if g of the first be added to of the second, the sum shall be 60.~ Prove by trial.

135. If the greater of two numbers be divided by the less, the quotient is 6, and the sum of the two numbers is 252. What are the numbers? Prove by trial.

136. A gentleman gave $4350 for a house-lot, the land being valued at $2 per foot. If it had been 6 feet wider, it would have cost $5394. What were the length and breadth of the lot? Prove by trial.

137. A boy bought at one time 5 apples, 6 pears, and 4 oranges, for 48 cents; at another time, 3 apples, 4 pears, and 5 oranges, for 43 cents; and again, 2 apples, 3 pears, and 6 oranges, for 43 cents, all at the same rate. What did he pay for each kind of fruit? Prove by trial.

138. There were 5 Sundays in the month of February in 1852. In what year will this occur again; that is, when will the first day of February fall on a Sunday in a bissextile or leap year? Ans. In 1880.

Suggestive Questions.-How many days of the week does the year advance from one bissextile to another? What is the smallest number of fives exactly divisible by 7? Then how many bissextiles must elapse till 5 Sundays again occur in February?

Equation of Payments.

139. A man bought a farm for $2000, one half of which was to be paid in two years, and the remainder in 4 years; that is, the purchaser was to have the use of $1000 of the purchase money for 2 years, and the use of the remaining

$1000 for 4

years.

At what time may the whole be paid at

once without loss to either of the parties?

Suggestive Questions.-How long must he keep the $2000 so as to balance the use of $6000 for one year? By what process can this be ascertained? By addition, subtraction, multiplication, or division?

140. A man owed his neighbor $300, which he engaged to pay as follows: $50 in 2 months, 100 in 4 months, and $150 in 6 months. When may the whole be paid at once without loss to either party?

Suggestive Question.-$1400 for 1 month=$300 for how many months?

141. A friend lent me $400 for three months. How long should I lend him $100 to balance the favor?

Ans. 12 months. 142. A man bought a piece of property for $600, and agreed to pay $100 in 2 months, 200 in 5 months, and the rest in 8 months? What would be the proper time to make one payment of the whole? Ans. 6 months.

143. What is the mean time for the settlement of a debt of $800, contracted to be paid as follows: $200 in 3 months, of the remainder in 4 months, of what then remains in months, and the rest in 6 months? Ans. 4 months.

144. One merchant owes another $800, payable in 6 months, but wishes to pay him $200 of the debt in 2 months. How long should the time of payment of the remainder be suspended to balance the favor? Ans. 11 months.

145. A country merchant makes purchases from a merchant in Boston, on a credit of 6 months, as follows: $1500

on May 1, $400 on June 1, $500 on July 1, and $300 on Aug. 1. What is the mean time for the whole from Aug. 1? Ans. 4 months.

146. What is the mean length of the following pieces of cloth: No. 1, 30 yds.; No. 2, 28 yds.; No. 3, 27 yds.; No. 4, 29 yds.; No. 5, 32 yds.; No. 6, 25 yds.; No. 7, 25 yds. Ans. 28 yards.

147. A man on horseback travelled the following distances: the first day, 30 miles; the second day, 34 miles; the third day, 36 miles; and the fourth day, 42 miles. How many miles did he average a day? Ans. 35 miles.

148. Four men are engaged in building a wall measuring 820 cubic feet. The first can build 9 cubic feet in 4 days; the second, 10 cubic feet in 4 days; the third, 8 cubic feet in 6 days; and the fourth, 7 cubic feet in 3 days. How many days. will be necessary to complete the whole wall, when all work together?

149. A merchant had 32 tons of plaster for sale. On examining his sale books at the end of a week, he found that there remained 8 tons more than he had sold. How many tons were sold? Prove.

150. Three farmers bought a pasture jointly, consisting of 140 acres. On dividing it, it was agreed that A's share should be to B's as 6 to 11, and that C should have 4 acres more than A and B together. What is the share of each? Prove.

151. A man being asked how much money he had in his pocket, answered that and of it amounted to $320. How much had he? Prove.

152. A traveller, being asked what o'clock it was, replied that it was between 3 and 4. But a more particular answer being requested, said that the hour and minute hands were exactly together. What was the time? Ans. 164 min. past 3.

Suggestive Questions.-How far are the hands apart at 3 o'clock ? In what time will the minute overtake the hour hand?

153. John sets out on a journey, and travels at the rate of 5 miles an hour. He travels He travels 8 hours the first day, and the next morning a friend sets out after him at the rate of 7 miles an hour. If both start at the same hour in the morning, and travel the same number of hours in a day, how far must the friend travel before he overtakes John?

154. How many miles an hour must William travel for 20 hours, in order to overtake John, who is 40 miles ahead, and is travelling at the rate of 5 miles an hour?

155. A company sets out for California by land, and travels at the rate of 30 miles a day. Three days afterwards a man undertook to overtake them, and accomplished his purpose in 10 days. At what rate per day did the man travel?

156. A man bound for California by land, on his arrival at the usual starting point, learns that a company was 3 days ahead of him, with the intention of travelling 30 miles a day. He set out after them, and travels at the rate of 39 miles a day. In how many days will he overtake them?

157. The velocity of sound through the air is found to be 1142 feet per second of time; and, in a healthy person, the number of pulsations is, say 70 in a minute. Now, between the time of observing a flash of lightning and hearing the explosion of the thunder I counted 20 pulsations. Required the number of feet which sound moves in a minute; the number in one pulsation; and the distance of the cloud in miles.

158. A gentleman counted 20 pulsations between the sight of a flash of lightning and the arrival of the sound. By calculation he found the distance of the cloud to be 3 miles, 226 rods, and 84 feet; allowing the pulsations to be at the rate of 70 in a minute, how many feet did the sound travel in a second?

159. A lunar month, in which the moon makes a complete apparent revolution round the earth, is, say 291 days. Supposing the moon's motion to be uniform, what is the apparent distance of the sun and moon in degrees, &c., in one day after the change? in 12 days 6 hours after the change? in 19 days? [Take notice that the moon again begins to approach the sun after 14 days. Why?] Ans. to the last question, 1288°

160. The earth, being 360° in circumference, turns on its axis, say in 24 hours. How many miles are the inhabitants at the equator carried by that movement in one minute, a degree there being 69 miles? Ans. 17g miles.

161. If an ingot of gold, weighing 9 lb. 9 oz. 12 dwt., be worth $1128'96, what is it worth per grain?

162. If gold be worth 2 cents per grain, what is the value of 9 lb. 9 oz. 12 dwt.?

163. A saves of his income; but B, who has the same